Table of Contents
Idempotent semirings with identity
Abbreviation: ISRng$_1$
Definition
An idempotent semiring with identity is a semirings with identity $\mathbf{S}=\langle S,\vee,\cdot,1 \rangle $ such that
$\vee$ is idempotent: $x\vee x=x$
Morphisms
Let $\mathbf{S}$ and $\mathbf{T}$ be idempotent semirings with identity. A morphism from $\mathbf{S}$ to $\mathbf{T}$ is a function $h:S\rightarrow T$ that is a homomorphism:
$h(x\vee y)=h(x)\vee h(y)$, $h(x\cdot y)=h(x)\cdot h(y)$, $h(1)=1$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr} f(1)= &1\\ f(2)= &1\\ f(3)= &\\ f(4)= &\\ f(5)= &\\ f(6)= &\\ \end{array}$
Subclasses
Superclasses
References
Trace: » idempotent_semirings_with_identity